Mathematical analysis of a generalised p53-Mdm2 protein gene expression model
Piotrowska, Monika J.; Bartłomiejczyk, Agnieszka; Bodnar, Marek
2018-07-01 00:00:00
•Generalization of the p53-Mdm2 protein gene expression model is presented.
•Existence of invariant set, uniqueness and global existence of solutions are proved.
•Conditions guaranteeing the existence of oscillatory solutions are given.
•Stability of the periodic solutions born due to the Hopf bifurcation is studied.
•Influence of the Hill coefficient in the Mdm2 mRNA production function is discussed.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngApplied Mathematics and ComputationElsevierhttp://www.deepdyve.com/lp/elsevier/mathematical-analysis-of-a-generalised-p53-mdm2-protein-gene-IvfH8R0iso

Abstract

•Generalization of the p53-Mdm2 protein gene expression model is presented.
•Existence of invariant set, uniqueness and global existence of solutions are proved.
•Conditions guaranteeing the existence of oscillatory solutions are given.
•Stability of the periodic solutions born due to the Hopf bifurcation is studied.
•Influence of the Hill coefficient in the Mdm2 mRNA production function is discussed.

Journal

Applied Mathematics and Computation
– Elsevier

Published: Jul 1, 2018

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References

A synthetic inhibitor of p53 protects neurons against death induced by ischemic and excitotoxic insults, and amyloid β-peptide